Theory and Applications of Computability
cover

Handbook of Computability and Complexity in Analysis

Editors: Brattka, Vasco, Hertling, Peter (Eds.)

  • Computability and complexity theory are two central areas of research in mathematical logic and theoretical computer science
  • Researchers and graduate students will appreciate the book's systematic introductions into many branches of computable analysis
  • Dedicated to Klaus Weihrauch, the leading pioneer and teacher in this domain
  • Further domain information available at http://cca-net.de/
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eBook 85,59 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: June 2, 2021
  • ISBN 978-3-030-59234-9
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover 103,99 €
price for Spain (gross)
  • Due: June 2, 2021
  • ISBN 978-3-030-59233-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s. This was motivated by questions such as: which real numbers and real number functions are computable, and which mathematical tasks in analysis can be solved by algorithmic means?

Nowadays this theory has many different facets that embrace topics from computability theory, algorithmic randomness, computational complexity, dynamical systems, fractals, and analog computers, up to logic, descriptive set theory, constructivism, and reverse mathematics. In recent decades computable analysis has invaded many branches of analysis, and researchers have studied computability and complexity questions arising from real and complex analysis, functional analysis, and the theory of differential equations, up to (geometric) measure theory and topology.

This handbook represents the first coherent cross-section through most active research topics on the more theoretical side of the field. It contains 11 chapters grouped into parts on computability in analysis; complexity, dynamics, and randomness; and constructivity, logic, and descriptive complexity. All chapters are written by leading experts working at the cutting edge of the respective topic. Researchers and graduate students in the areas of theoretical computer science and mathematical logic will find systematic introductions into many branches of computable analysis, and a wealth of information and references that will help them to navigate the modern research literature in this field.

About the authors

Vasco Brattka is a professor for Theoretical Computer Science and Mathematical Logic at the Universität der Bundeswehr München and an Honorary Research Associate at the University of Cape Town. He is the Editor-in-Chief of Computability, the journal of the association, Computability in Europe, published by IOS Press. His research interests include computable analysis, computability theory, effective descriptive set theory, algorithmic randomness, complexity and logic, and Weihrauch complexity. 
Peter Hertling is a professor in the Institut für Theoretische Informatik, Mathematik und Operations Research at the Universität der Bundeswehr München. He is an Associate Editor of the Journal of Complexity, published by Elsevier. His research interests include computable analysis, descriptive complexity and algorithmic randomness, complexity theory over the real numbers, and information-based complexity.

Buy this book

eBook 85,59 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: June 2, 2021
  • ISBN 978-3-030-59234-9
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover 103,99 €
price for Spain (gross)
  • Due: June 2, 2021
  • ISBN 978-3-030-59233-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Handbook of Computability and Complexity in Analysis
Editors
  • Vasco Brattka
  • Peter Hertling
Series Title
Theory and Applications of Computability
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-59234-9
DOI
10.1007/978-3-030-59234-9
Hardcover ISBN
978-3-030-59233-2
Series ISSN
2190-619X
Edition Number
1
Number of Pages
XXIV, 426
Number of Illustrations
23 b/w illustrations
Topics